ADHM construction of perverse instanton sheaves

TL;DR

This paper generalizes the ADHM construction to produce and classify perverse instanton sheaves on various projective varieties, extending known results from projective spaces and providing a categorical framework.

Contribution

It introduces a generalized ADHM construction for perverse instanton sheaves on diverse projective varieties and describes their moduli spaces and categorical properties.

Findings

Moduli space of these sheaves is a quasi projective variety.

Construction extends to varieties containing a fixed line.

Categorical and hypercohomological descriptions provided.

Abstract

We present a construction of framed torsion free instanton sheaves on a projective variety containing a fixed line which further generalizes the one on projective spaces. This is done by generalizing the so called ADHM variety. We show that the moduli space of such objects is a quasi projective variety, which is fine in the case of projective spaces. We also give an ADHM categorical description of perverse instanton sheaves in the general case, along with a hypercohomological characterization of these sheaves in the particular case of projective spaces.